Abstract
The general definition of deformation twinning in a crystal is that a region undergoes a homogeneous shear in such a way that the structure is reproduced in a new orientation. An algebraic formulation of a twinning shear S, which is consistent with this definition is obtained by letting S = RU, where R represents a rigid body rotation and U a deformation which deforms the lattice into itself. The equation S = RU has been used as the basis of an analysis which enables possible twinning shears to be determined for a particular choice of matrix U. Unlike other theories of the crystallography of deformation twinning the analysis does not restrict the orientation relationship between twin and parent lattices to an element, of symmetry. The analysis has been applied to the cubic, tetragonal, orthorhombic, hexagonal and rhombohedral Bravais lattices. In all cases non-conventional as well as conventional shears have been deduced. The analysis and its application to the forementioned Bravais lattices are presented in Part I of this thesis. Two new single surface trace analyses are presented in Part II. The first enables the orientation of rhombohedral and cubic crystals to be determined from the traces produced by the intersection of three crystallographically equivalent and symmetrically disposed planes with the flat surface of the crystal. The second analysis enables both the orientation and thickness of thin films used in transmission electron microscopy to be determined from a knowledge of the projected trace widths of two known planes and their included angle.